Binomial series as Maclaurin's series

Suppose \(n \in \mathbb{Q}\). The Binomial Theorem can be generalized to the following:

\[(a+b)^n = a^n \left( 1 + n \left( \frac{b}{a} \right) + \frac{n(n-1)}{2!} \left( \frac{b}{a} \right)^2 + \dots \right)\]

Notes:

1. This is an infinite series.
2. This is only valid for \(\left| \frac{b}{a} \right| < 1\).
3. The derivation makes use of the Maclaurin series expansion.